Modern decorating schemes commonly call for the coordination of relatively small accessory items with other decorative elements. For example, a wastebasket for a bedroom may be provided with a cover that matches the drapes and/or comforter in the room. Similarly, a wastebasket and a tissue box for the bathroom may be provided with covers matching a shower curtain. There are presently covers for accessory items of this type available on the market. One type of cover for a wastebasket has a stiff bottom and stiff pleated sidewalls into which a basic wastebasket liner is inserted. This type of cover presents a highly attractive and high quality appearance because the folding or pleating of the cover sidewall is always neatly presented. However, the cover has the disadvantages of being relatively expensive and of having little, if any, flexibility in the choice of the wastebasket liner. It also cannot be machine washed and is not foldable for shipping. Another type of cover that is available on the market has a soft fabric bottom as well as a soft fabric sidewall. This product is foldable, may be machine washable, and is less expensive and more versatile in the type of liner it will accept, but these characteristics are achieved at the expense of the neat appearance of the type of cover with a stiff bottom and a stiff sidewall.